Hi Andy,
Your revolver is a wartime issue Model of 1905 4th Change Smith & Wesson Military & Police revolver, also known as a Victory Model. It is chambered in .38 Special. The U.S.NAVY stamp on the topstrap appears to be absolutely authentic. Still, a letter from Roy Jinks will be indisputable verification of your revolver's history. His letter will also tell you exactly when it left Smith & Wesson and to which duty station/armory and perhaps even the supply officer it was shipped.
The finish appears to be pristine. Unfortunately, the rust speckles need to be contended with. You should immediately oil the finish on this gun. If you have a good gun oil such as Break Free or Ballistol, use it. If not, any oil other than WD-40 will be fine, including motor oil.
Remove the grips before oiling the gun by loosening the screw and using it to push the opposite grip off the frame. Then push the center of the remaining grip to remove it as well. Do not pry them off. You will find the serial number inside one of the grips.
Do not lossen the screws holding the sideplate on or attempt to remove it unless you know what you are doing and have the correct tools. Damaging the screws will lower the value. Prying off the sideplate will ruin it's fit and likewise lower the value of this revolver.
The pitting on the butt and lanyard loop is a bit of a problem, as is the rust. The rust speckles can be removed, once the gun is oiled and the rust softened with the oil. Use a copper penny to scrape the rust off. The copper will not damage the finish.
Do not use anything steel. If you even think about refinishing it, go pick up a ball peen hammer and hit your forehead until the idea has vanished.
If you would like tro replace the pitted lanyard loop, they can still be found in NOS condition. They usually sell for $10-15 each in that shape.
Where I am at, this revolver would bring $400 as it is. Once it is cleaned up, and with a
letter from Roy Jinks authenticating it as a Navy Victory, it is a $500 revolver, easily. Over the next decade or two, you can expect the market value of this revolver to increase dramatically.
Assuming the old vet who brought it home is still with us, I would also urge you to record any stories he has of the revolver, including how he brought it home in his hat. Have him sign this, notarize it, and take a good photo of him with the revolver. If you have any photos of him while he was in the Navy, particularly in uniform, get copies to include in the package. What you are holding is a part of history. You don't want that history to be lost.
Congratulations on a beautiful Smith & Wesson Navy Victory Model!